Simplify the following expression: $\dfrac{132a^3}{144a^5}$ You can assume $a \neq 0$.
Solution: $ \dfrac{132a^3}{144a^5} = \dfrac{132}{144} \cdot \dfrac{a^3}{a^5} $ To simplify $\frac{132}{144}$ , find the greatest common factor (GCD) of $132$ and $144$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(132, 144) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{132}{144} \cdot \dfrac{a^3}{a^5} = \dfrac{12 \cdot 11}{12 \cdot 12} \cdot \dfrac{a^3}{a^5} $ $\phantom{ \dfrac{132}{144} \cdot \dfrac{3}{5}} = \dfrac{11}{12} \cdot \dfrac{a^3}{a^5} $ $ \dfrac{a^3}{a^5} = \dfrac{a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a} = \dfrac{1}{a^2} $ $ \dfrac{11}{12} \cdot \dfrac{1}{a^2} = \dfrac{11}{12a^2} $